Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity

2016/01/31 by Thibault Damour, P. Jaranowski, Piotr Jaranowski +1 · 8 citations
Mathematics · Physics and Astronomy · #Action (physics) #Applied mathematics #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Cosmology and Gravitation Theories #Delaunay triangulation #Einstein #General relativity #Geometry #Gravitation #Hamiltonian (control theory) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Physics #Piecewise #Pulsars and Gravitational Waves Research #Quantum mechanics #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.93.084014

published as Phys. Rev. D 93, 084014 (2016) · Additional discussion of Fokker-type actions in Appendix A; new references added; identical to published version; 20 pages

openalex publication_date 2016/04/08 · arxiv created 2016/04/27 · arxiv updated 2016/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The fourth post-Newtonian (4PN) two-body dynamics has been recently tackled by several different approaches: effective field theory, Arnowitt-Deser-Misner Hamiltonian, action-angle-Delaunay averaging, effective-one-body, gravitational self-force, first law of dynamics, and Fokker action. We review the achievements of these approaches and discuss the complementarity of their results. Our main conclusions are: (i) the results of the first complete derivation of the 4PN dynamics [T. Damour, P. Jaranowski, and G. Sch"afer, Phys. Rev. D 89, 064058 (2014)] have been, piecewise, fully confirmed by several subsequent works; (ii) the results of the Delaunay-averaging technique [T. Damour, P. Jaranowski, and G. Sch"afer, Phys. Rev. D 91, 084024 (2015)] have been confirmed by several independent works; and (iii) several claims in a recent harmonic-coordinates Fokker-action computation [L. Bernard et al., arXiv:1512.02876v2] are incorrect, but can be corrected by the addition of a couple of ambiguity parameters linked to subtleties in the regularization of infrared and ultraviolet divergences.

Citations

• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Tail terms in gravitational radiation reaction via effective field theory
• Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
• Dimensional regularization of the gravitational interaction of point masses
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• Testing gravity to second post-Newtonian order: A field-theory approach
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Effective one-body approach to general relativistic two-body dynamics
• Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry

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• Three-body effective potential in general relativity at second post-Minkowskian order and resulting post-Newtonian contributions
• Analytic approximations in GR and gravitational waves
• Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio
• Equations of motion of self-gravitatingN-body systems in the first post-Minkowskian approximation